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          KMP算法
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        <h3 id="简介"><a href="#简介" class="headerlink" title="简介"></a>简介</h3><p>KMP算法是三位提出者名字首字母的简写，主要是用于给定字符串和模式串<br>的加速匹配，消除匹配时不必要的指针回溯，从而使算法效率得到提高。<br>KMP算法的核心是计算出模式串的next数组。<a id="more"></a></p>
<h3 id="next数组"><a href="#next数组" class="headerlink" title="next数组"></a>next数组</h3><p>要计算next数组，首先要明确next数组的含义。</p>
<p>next数组下标：表示已匹配前缀的下一个位置</p>
<p>next数组元素的值：表示最长可匹配的前缀子串的下一个位置</p>
<p>并且为了方便计算，next[0]=-1;</p>
<p>思路：</p>
<p>首先设置<code>k , j</code> 两个指针指向next数组下标，同时为了方便计算令 <code>j = 0, k = -1</code>； </p>
<p>接着对模式串进行遍历，如果是<code>k = -1 或者 下标k 和 j的元素相等</code>，就分别对j 和 k 加 1 ，再把 k 的值赋给next数组中 j 下标的元素；否则就对<code>k</code>进行回溯，找出可能存在的短的可匹配前缀。</p>
<p>next方法实现：</p>
<figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br></pre></td><td class="code"><pre><span class="line"><span class="function"><span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">void</span> <span class="title">next</span><span class="params">(String s, <span class="keyword">int</span>[] next)</span></span>&#123;</span><br><span class="line">        <span class="keyword">int</span> len = s.length();</span><br><span class="line">        next[<span class="number">0</span>] = -<span class="number">1</span>;</span><br><span class="line">        <span class="keyword">int</span> k = -<span class="number">1</span>;</span><br><span class="line">        <span class="keyword">int</span> j = <span class="number">0</span>;</span><br><span class="line">        <span class="keyword">while</span> (j &lt; len) &#123;</span><br><span class="line">            <span class="keyword">if</span> (k == -<span class="number">1</span> || s.charAt(j) == s.charAt(k)) &#123;</span><br><span class="line">                j++;</span><br><span class="line">                k++;</span><br><span class="line">                next[j] = k;</span><br><span class="line">            &#125; <span class="keyword">else</span> &#123;</span><br><span class="line">                k = next[k];	<span class="comment">//next方法的核心</span></span><br><span class="line">            &#125;</span><br><span class="line">        &#125;</span><br><span class="line">    &#125;</span><br></pre></td></tr></table></figure>




<h3 id="KMP实现"><a href="#KMP实现" class="headerlink" title="KMP实现"></a>KMP实现</h3><figure class="highlight java"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br></pre></td><td class="code"><pre><span class="line"><span class="function"><span class="keyword">public</span> <span class="keyword">static</span> <span class="keyword">int</span> <span class="title">kmp</span><span class="params">(String s, String t)</span></span>&#123;</span><br><span class="line">        <span class="keyword">int</span>[] next = <span class="keyword">new</span> <span class="keyword">int</span>[t.length() + <span class="number">1</span>];</span><br><span class="line">        <span class="keyword">int</span> i = <span class="number">0</span>;</span><br><span class="line">        <span class="keyword">int</span> j = <span class="number">0</span>;</span><br><span class="line">        next(t, next);</span><br><span class="line">        <span class="keyword">while</span> (i &lt; s.length() &amp;&amp; j &lt; t.length()) &#123;</span><br><span class="line">            <span class="keyword">if</span>(j == -<span class="number">1</span> || s.charAt(i) == t.charAt(j))&#123;</span><br><span class="line">                i++;</span><br><span class="line">                j++;</span><br><span class="line">            &#125;<span class="keyword">else</span> &#123;</span><br><span class="line">                j = next[j];</span><br><span class="line">            &#125;</span><br><span class="line">        &#125;</span><br><span class="line">        <span class="keyword">if</span> (j &gt;= t.length()) &#123;</span><br><span class="line">            <span class="keyword">return</span> (i - t.length());    <span class="comment">//匹配成功，返回第一次匹配成功的子串位置</span></span><br><span class="line">        &#125;<span class="keyword">else</span> &#123;</span><br><span class="line">            <span class="keyword">return</span> (-<span class="number">1</span>);                <span class="comment">//没找到</span></span><br><span class="line">        &#125;</span><br><span class="line">    &#125;</span><br></pre></td></tr></table></figure>



<p>要彻底了解 KMP 算法，光是看看别人的分析或许还不行，最重要的还是要自己通过一步步的运算，找出其中的关系，这样再返回来理解代码就比较容易了。</p>
<p><a href="https://blog.csdn.net/dark_cy/article/details/88698736" target="_blank" rel="noopener">详细过程参考这里</a></p>

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